Problem: Given $ m \angle MON = 7x + 77$, and $ m \angle LOM = 8x - 77$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {8x - 77} + {7x + 77} = {180}$ Combine like terms: $ 15x + 0 = 180$ Add $0$ to both sides: $ 15x = 180$ Divide both sides by $15$ to find $x$ $ x = 12$ Substitute $12$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 8({12}) - 77$ Simplify: $ {m\angle LOM = 96 - 77}$ So ${m\angle LOM = 19}$.